The 29-year-old joined Celtic on loan in the January transfer window, despite also being linked with a move to Sunderland.
The Daily Mirror reports that Sunderland owner Ellis Short is prepared to fund another spending spree and allow Bruce to make an £8million bid for Keane.
The Black Cats are also prepared to pay £3.5million for Alan Hutton, who has been on loan at the club from Spurs.
